quench

COPPER_DENSITY = 8960.0 module-attribute

NB3SN_DENSITY = 8040.0 module-attribute

calculate_quench_protection_current_density(tau_discharge, peak_field, f_cu, f_he, t_he_peak, t_max, cu_rrr, detection_time, fluence)

Calculates the current density limited by the protection limit.

Simplified 0-D adiabatic heat balance "hotspot criterion" model.

Uses temperature- and magnetic field-dependent material properties to determine the maximum allowable winding pack current density during a quench. Assumes that the magnetic field does not decay over time and accounts for contributions from copper, helium, and superconductor materials using temperature integrals.

Parameters:

Name	Type	Description	Default
tau_discharge	float	tau_discharge: Quench discharge time constant [s].	required
peak_field	float	peak_field: Magnetic field at the peak point [T].	required
f_cu	float	f_cu: Fraction of conductor cross-section that is copper.	required
f_he	float	f_he: Fraction of cable occupied by helium.	required
t_he_peak	float	t_he_peak: Peak helium temperature at quench initiation [K].	required
t_max	float	t_max: Maximum allowed conductor temperature during quench [K].	required
cu_rrr	float	cu_rrr: Residual resistivity ratio of copper.	required
detection_time	float	detection_time: Detection time delay [s].	required
fluence	float	fluence: Neutron fluence [n/m²].	required

Returns:

Type	Description
float	Maximum allowable winding pack current density [A/m²].

Notes

• Assumes constant magnetic field over the duration of the quench.
• Assumes the dump resistor has a constant resistance much higher than that of the TF coil.
• Operates on the current-carring cross-section of a conductor. The jacket and insulation are ignored. The actual allowable WP current density must be weighted with the ratio of current-carrying cross-section vs. total WP cross-section (including jacket and insulation).
• Presently only applicable to LTS TF coil winding packs (Nb3Sn assumed)

Source code in process/models/tfcoil/quench.py

def calculate_quench_protection_current_density(
    tau_discharge: float,
    peak_field: float,
    f_cu: float,
    f_he: float,
    t_he_peak: float,
    t_max: float,
    cu_rrr: float,
    detection_time: float,
    fluence: float,
) -> float:
    """Calculates the current density limited by the protection limit.

    Simplified 0-D adiabatic heat balance "hotspot criterion" model.

    Uses temperature- and magnetic field-dependent material properties to determine the
    maximum allowable winding pack current density during a quench. Assumes that the magnetic
    field does not decay over time and accounts for contributions from copper, helium, and
    superconductor materials using temperature integrals.


    Parameters
    ----------
    tau_discharge:
        tau_discharge: Quench discharge time constant [s].
    peak_field:
        peak_field: Magnetic field at the peak point [T].
    f_cu:
        f_cu: Fraction of conductor cross-section that is copper.
    f_he:
        f_he: Fraction of cable occupied by helium.
    t_he_peak:
        t_he_peak: Peak helium temperature at quench initiation [K].
    t_max:
        t_max: Maximum allowed conductor temperature during quench [K].
    cu_rrr:
        cu_rrr: Residual resistivity ratio of copper.
    detection_time:
        detection_time: Detection time delay [s].
    fluence:
        fluence: Neutron fluence [n/m²].

    Returns
    -------
    float
        Maximum allowable winding pack current density [A/m²].

    Notes
    -----
    - Assumes constant magnetic field over the duration of the quench.
    - Assumes the dump resistor has a constant resistance much higher
    than that of the TF coil.
    - Operates on the current-carring cross-section of a conductor. The
    jacket and insulation are ignored. The actual allowable WP current
    density must be weighted with the ratio of current-carrying cross-section
    vs. total WP cross-section (including jacket and insulation).
    - Presently only applicable to LTS TF coil winding packs (Nb3Sn assumed)
    """
    # Default fluence is too high for this model
    if (fluence < 0.0) | (fluence > 1.5e23):
        warn("Fluence values out of range [0.0, 1.5e23]; kludging.", stacklevel=2)
        fluence = np.clip(fluence, 0.0, 1.5e23)

    i_he, i_cu, i_sc = _quench_integrals(t_he_peak, t_max, peak_field, cu_rrr, fluence)

    f_cond = 1.0 - f_he  # Fraction of the cable XS area that is not helium
    f_cu_cable = f_cond * f_cu  # Fraction of the cable XS that is copper
    f_sc_cable = f_cond * (1.0 - f_cu)  # Fraction of the cable XS that is superconductor

    factor = 1.0 / (0.5 * tau_discharge + detection_time)
    total_integral = f_he * i_he + f_cu_cable * i_cu + f_sc_cable * i_sc

    return np.sqrt(factor * f_cu_cable * total_integral)